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Dynamic Coherent Risk Measures

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Frank Riedel

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Abstract

January 2003

In this paper, a notion of risk measure is defined for dynamic models. Three axioms, coherence, relevance and dynamic consistence, are postulated. It is shown that every dynamic risk measure that satisfies the axioms can be represented as the maximal expected present value of future losses where expectations are taken with respect to a set of probability measures. As new information arrives, this set of probability measures is updated in the Bayesian way. Moreover, dynamic consistency implies that this set satisfies a certain consistency condition.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 03004.

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Date of creation: Jan 2003
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Handle: RePEc:wop:stanec:03004

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  1. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
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  2. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482. [Downloadable!] (restricted)
  3. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November. [Downloadable!] (restricted)
  4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
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  1. Volker Krätschmer, 2007. "On s-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model," SFB 649 Discussion Papers SFB649DP2007-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA. [Downloadable!]
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